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In this paper, we establish the existence and uniqueness of extremal solutions for nonlinear boundary value problems of a singular fractional p-Laplacian differential equation involving Riemann-Liouville derivatives. Our results are obtained by constructing monotone iterative sequences of upper and lower solutions and applying the comparison result. At last, we present an example to illustrate the results. The compactness of sequences is proved in the Appendix.

In this paper, a combined error model for thermal error compensation of machine tools is presented. Through the analysis of thermal error data of machine spindle at different temperatures, the error variation law is obtained. Experiments on the axial directional spindle deformation on a CNC machine center are conducted to build and validate the proposed models. The experimental validations show that the thermal errors of the machine tool are reduced effectively after applying the error compensation approach. The combined error model performs better than the traditional time series and neural network model in terms of prediction accuracy and robustness, which means that the new model is more suitable for complex working conditions in industrial applications.